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Title:

The complete classification of five-dimensional Dirichlet - Voronoi polyhedra of translational lattices

Document type:
Zeitschriftenaufsatz
Author(s):
Dutour Sikirić, Mathieu and Garber, Alexey and Schürmann, Achill and Waldmann, Clara
Non-TUM Co-author(s):
ja
Cooperation:
international
Abstract:
This paper reports on the full classification of Dirichlet{--}Voronoi polyhedra and Delaunay subdivisions of five-dimensional translational lattices. A complete list is obtained of 110244 affine types ({\it L}-types) of Delaunay subdivisions and it turns out that they are all combinatorially inequivalent, giving the same number of combinatorial types of Dirichlet{--}Voronoi polyhedra. Using a refinement of corresponding secondary cones, 181394 contraction types are obtained. The paper gives deta...     »
Keywords:
Dirichlet-Voronoi polytope, Delaunay polytope, secondary cones, affine types, contraction types, topological mass formula, combinatorial enumeration
Intellectual Contribution:
Discipline-based Research
Journal title:
Acta Crystallographica Section A
Journal listet in FT50 ranking:
nein
Year:
2016
Journal volume:
72
Month:
Nov
Journal issue:
6
Pages contribution:
673--683
Fulltext / DOI:
doi:10.1107/S2053273316011682
Judgement review:
0
Key publication:
Ja
Peer reviewed:
Ja
International:
Ja
Book review:
Nein
Commissioned:
not commissioned
Professional Journal:
Nein
Interdisciplinarity:
Nein
Mission statement:
;
Ethics and Sustainability:
Nein
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